Posts by gjm@mathstodon.xyz
(DIR) Post #AVb3xwZTIEZYsEhBnk by gjm@mathstodon.xyz
2023-03-05T12:00:36Z
1 likes, 0 repeats
@gregeganSF My super-handwavy argument: _given_ the (to me surprising) fact that the PE is orientation-independent in a uniform field, what's different in a 1/r^2 field? Answer: moving points "outward" increases their PE, by a larger extent as you move "downward" where the field is curvier.So the difference between vertex-up and vertex-down, _relative to a uniform field_, is that the extra horizontal spread happens further up (where it makes less difference) for vertex-down and further down (where it makes more difference) for vertex-up. So vertex-down must be better.If this argument is valid (which it might not be; I haven't thought about it super-hard) it should apply to _any_ field where the PE is of the form f(r) with f monotone decreasing.
(DIR) Post #Aj1ozhNahgx2K00izA by gjm@mathstodon.xyz
2024-06-17T14:09:11Z
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@hananc @llewelly @futurebird @SmudgeTheInsultCat I have heard it claimed that in China they say something like "it is the language of heaven". I don't know whether that's true (it seems a bit too much like the sort of thing someone not-Chinese might think the Chinese would say).Relatedly, I wonder whether the graph is acyclic. That is, does it ever happen that country A regards country B's language as stereotypically incomprehensible, and country B thinks the same about country C, etc., until eventually we end up back with A again?
(DIR) Post #Aj1ozjivzJDDam0nWy by gjm@mathstodon.xyz
2024-06-17T14:12:20Z
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@hananc @llewelly @futurebird @SmudgeTheInsultCat The graph at https://flowingdata.com/2015/04/14/its-all-greek-or-chinese-or-spanish-or-to-me/ suggests that at least some Chinese speakers use English in their version of this idiom, which if I'm reading their graph correctly makes English -> Greek -> Chinese -> English a possible cycle.
(DIR) Post #An51jss20ZSBUXE2gi by gjm@mathstodon.xyz
2024-10-17T00:08:41Z
0 likes, 1 repeats
@futurebird You don't want to do this by factorizing (which can be expensive).If N = (n choose r) then also N = (n choose n-r), so it's OK only to look at solutions with r <= n-r or equivalently n >= 2r.If N = (n choose r) with n >= 2r then for sure N >= (2r choose r). This is a fairly rapidly increasing function of r, so we can quickly get an upper bound on how big r is, and it won't be very big unless N is enormous.Now we can just try each value of r. We have r! N = r! (n choose r) = n(n-1)(n-2)...(n-r+1), the product of n consecutive integers with the largest being n. This is always somewhere between (n-r+1)^r and n^r, so t := (r! N)^(1/r) is somewhere between n-r+1 and n, so n is somewhere between t and t+r-1. Now we can try them all or do a binary search or something. (We can surely do better but this is easy and efficient enough.) Unless we are unlucky, we will be able to reject most r quickly by observing that ceiling(t) is always one of those consecutive integers, so we can rule out any r for which N isn't a multiple of ceiling((r! N)^(1/r)).So let's look at 7413705167549733. (56 choose 28) is bigger than this, so we can restrict ourselves to r <= 27. If I haven't screwed up my calculations, it turns out that 7413705167549733 isn't a multiple of ceiling(t) for any choice of r other than r=1. So that number isn't nontrivially a binomial coefficient.
(DIR) Post #AoSm1FTn6uIvi1xYAK by gjm@mathstodon.xyz
2024-11-27T00:45:50Z
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@ColinTheMathmo Carlo Rovelli, _The Order of Time_. p42 sentence 2:It makes no sense to ask whether is is Cleomenes or Gorgo who is "of the same generation" as Leonidas, because there is no single concept of "same generation".Whether that's "nearest" depends on what part of my body you measure from. Other candidates, all of which could be considered "nearest" by some definition, from the same stack of recently purchased books:Lewis Wolpert, _The Unnatural Nature of Science_: "Do most of us, lying in our baths, understand that our loss of weight is equal to the weight of water we displace?"Kelly & Zach Weinersmith, _Soonish_: "Right now space tourism is so expensive and so controlled that (as far as we can tell) all the private space people are slightly crazy, very nerdy billionaires."Donald Knuth, _TAOCP_ vol 4B: "And the TAIL pointers, which indicate the current list sizes as in (19)-(23), are respectively kept in MEM locations [...]." (Technical details elided.)Dasgupta, Papadimitriou & Vazirani, _Algorithms_: "If p is prime, then we know every number 1 <= x < p is invertible modulo p." (It's part of an exercise.)Not all of my books are this nerdy, but these are the ones that happen to be physically nearest me right now.
(DIR) Post #At3BPdb6egW9zfmEnw by gjm@mathstodon.xyz
2025-04-13T14:00:11Z
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@futurebird This is hilarious but alas it can't be the original Nipper, who died three years before the first version of the painting that was adapted to make the "His Master's Voice" image.
(DIR) Post #AyAExIB8NjyOlKmXlw by gjm@mathstodon.xyz
2025-09-08T12:28:34Z
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@blog A bit of pedantry: _Programming Pearls_ is the title of Bentley's column in CACM and of a book collected from those columns.The collection of aphorisms here was _one_ of his columns. (That is, these things aren't the "pearls"; all of them collectively are one pearl.)That column isn't one of the ones that appeared in the book called _Programming Pearls_. It's in the sequel _More Programming Pearls_, published in 1988; what was published in 1985 was the "Bumper-Sticker Computer Science" column.
(DIR) Post #AzsZMKYuIVGe0cVNkO by gjm@mathstodon.xyz
2025-11-03T19:48:37Z
1 likes, 0 repeats
@josh My brother-in-law has at least once complained about being required to do "sexual harassment training" without any word like "awareness" or "prevention" in it, so yes.
(DIR) Post #B2UPsC2Wjg2QvGemLA by gjm@mathstodon.xyz
2026-01-20T20:40:07Z
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@neauoire @andnull I suspect DLL's comment is a deliberate reference to this, but in case (1) it isn't or (2) others didn't notice, Raymond Smullyan wrote a whole book with this premise: https://en.wikipedia.org/wiki/To_Mock_a_Mockingbird